The surface morphology of Ti-Mg supported catalyst and the polyethylene particles are studied usingscanning electron microscope(SEM) technology. The results show that either the catalysts surface or polymerparticles surface is irregular and has fractal characteristics, which can be described by fractal parameter. The moreinteresting discovery is that the surface fractal dimension values of the polymer particles vary periodically with thepolymerization time. We call this phenomenon fractal evolution, which can be divided into the "revolution" stageand the "evolution" stage. And then we present polymerization fractal growing model (PFGM), and successfullydescribe and/or predict the whole evolving process of the polyethylene particle morphology. under the different slurrypolymerization (including pre-polymerization) conditions without H2.